\(\int \frac { \mathrm { e } ^ { 2 x } + 6 } { \mathrm { e } ^ { 2 x } } \mathrm {~d} x\),
\(\int 3 \cos ^ { 2 } x \mathrm {~d} x\).
Use the trapezium rule with 2 intervals to estimate the value of
$$\int _ { 1 } ^ { 2 } \frac { 6 } { \ln ( x + 2 ) } \mathrm { d } x$$
giving your answer correct to 2 decimal places.
Express \(3 \cos \theta + \sin \theta\) in the form \(R \cos ( \theta - \alpha )\), where \(R > 0\) and \(0 ^ { \circ } < \alpha < 90 ^ { \circ }\), giving the exact value of \(R\) and the value of \(\alpha\) correct to 2 decimal places.
Hence solve the equation
$$3 \cos 2 x + \sin 2 x = 2$$
giving all solutions in the interval \(0 ^ { \circ } \leqslant x \leqslant 360 ^ { \circ }\).